John A. McCorquodale

Hydraulic Conductivity Of Rockfill

Dimensionless equations for the hydraulic conductivity of crushed rock and river gravel have been developed on the basis of approximately 1250 permeameter tests. Experimental data of a number of researches were used in the correlations. Grain sizes varied from .55 to .79 mm and pore Reynolds numbers were in the range of .001 to 20,000. The data are divided into two flow regimes and separate equations are proposed for each regime. Surface roughness is incorporated in the equations for the high Reynolds number regime. The correlations also account for the wall effect.

Effects of hydraulic and solids loading on clarifier performance

A numerical model for an idealized circular tank with no baffle is used to investigate the relative importance of inlet solids concentration and inlet flow on the removal of solids field. Effluent concentration is very sensitive to the velocities in the withdrawal zone. The densimetric Froude number relates hydraulic and solids loading. It was found that the upward velocities in the withdrawal zone increase with decreasing densimetric Froude number for a constant discharge. Under constant solids loading there is an optimum densimetric Froude number for minimum effluent concentration. The performance of the clarifier is a function of the densimetric Froude number and the return activated sludge ratio. For the clarifier considered here, the minimum effluent concentration for a constant solids loading, occurred at a densimetric Froude number of about 0.5. The Reynolds number, when in the turbulent regime, did not significantly affect the tank hydrodynamics. The predicted solids distribution was in good agree...

Hydraulic jumps on adverse slopes

The adverse hydraulic jump has been investigated and analyzed in order to derive the limiting design parameters for this type of jump. The limiting design condition refers to the adverse jump when it occurs entirely on the adverse slope; as such, this jump was difficult to establish at Froude numbers less than 9 and required continuous tailwater adjustment to maintain a stationary position for Froude numbers less than about 4. It was found that the sequent depth as well as the roller length for the adverse hydraulic jump is less than that for a horizontal jump with the same approach conditions. The results for the limiting adverse jump are compared with published results on a stabilized jump that starts on a positive slope and ends on an adverse slope. A momentum based theory is presented to determine the sequent depth ratio. An empirical equation is presented for the roller length.

Short-term local scour

Local scour downstream of an apron with a swept-out hydraulic jump is shown to develop very rapidly, that is in less than 1% of the time to reach the ultimate scour depth. The short-term scour although not as deep as the long-term scour, occurs much closer to the apron. The limiting short-term scour depth is found to be related to flow regime or type of hydraulic jump that dominates the flow in the scour hole. The deepest shortterm scour was associated with the plunging jump (B-jump) and the adverse jump regimes. A modification of the B-jump equation of Hager and Bretz is proposed to estimate the limiting depth of short-term local scour.

Numerical simulation of rectangular settling tanks

A numerical model to simulate the performance of primary clarifiers, with emphasis on the prediction of the velocity field and concentration distribution, is presented. The model is restricted to those mean steady flows which are isothermal, neutral density, low in solids concentration and nearly two-dimensional. The model employs the Strip Integral Method (SIM) to solve the governing differential equations of continuity, momentum and mass transport. This method is an improvement over the plug flow models in that it can reproduce the main features of the flow such as the boundary layer, recirculation and distribution of the dispersion coefficient. It has an advantage over the finite element and the finite difference models since it requires relatively low computer storage and computational time. The hydrodynamic submodel was calibrated using measured velocity distribution in a physical model. The model was used to simulate the rectangular clarifiers used in the City of Sarnia, Ontario, Canada. The predict...

Finite Element Circulation Model for Lake St. Clair

In the numerical modeling of a toxic chemical in a lake, it is necessary to solve the hydrodynamics of the transporting flow as well as the transformation processes of the pollutant in the lake. It is important to calibrate and verify the model before predictive applications. A simple numerical hydrodynamic model which includes wind stress, bottom friction, Coriolis force, inflow, outflow, and the bottom topography of the lake has been developed and verified with field data for Lake St. Clair. The overall root mean square differences between predicted and measured current magnitudes and directions were 1.30 cm s-1 and 22.5°, respectively, while the correlation coefficients were 0.99 and 0.95, respectively. The hydrodynamic model was tested for stability, convergence, and sensitivity to parameters such as wind shear, wind direction, and vertical eddy viscosity effects. This model is used to generate the typical lake circulation patterns for different steady state wind and ice conditions that are required for the long-term pollutant simulation models such as the EPA (TOXIWASP) model. The depth average velocities were also used in a finite element pollutant transport model. An upwind finite element formulation was used to obtain a stable solution for the convective transport phenomena. The predicted pollutant (chloride ion) concentration pattern was compared with observed field data and fairly good agreement was obtained.

Simulation of the radial hydraulic jump

The radial hydraulic jump has been simulated using a strip integral mathematical model. The model is calibrated against the writers experimental data. The strip integral method uses velocity shape functions to permit the partial integration of the equations of motion. A Gaussian velocity distribution is used in the mixing zone and the power law is used in the inner layer. The mathematical model includes the bed shear, turbulent shear, the potential core, entrained air, centrifugal force and turbulence pressure. The strip integral method has been applied to obtain a set of first order ordinary differential equations to describe the internal velocity distribution and water surface profile for a diverging radial hydraulic jump. These differential equations are solved by a fifth order Runge-Kutta method.

Modelling of flow in rectangular sedimentation tanks by an explicit third-order upwinding technique

SUMMARY A new numerical model has been developed to simulate the transport of dye in primary sedimentation tanks operating under neutral density conditions. A multidimensional algorithm based on a new skew third-order upwinding scheme (STOUS) is used to eliminate numerical diffusion. This algorithm introduces cross-difference terms to overcome the instability problems of the componentwise one-dimensional formlae for simulating multidimensional flows. Small physically unrealistic overshooting and undershooting have been avoided by using a well-established technique known as the universal limiter. A well-known rotating velocity field test was used to show the capability of STOUS in eliminating numerical diffusion. The STOUS results are compared with another third-order upwinding technique known as UTOPIA. The velocity field is obtained by solving the equations of motion in the vorticity‐streamfunction formulation. A k‐ model is used to simulate the turbulence phenomena. The velocity field compares favourably with previous measurements and with UTOPIA results. An additional differential equation governing the unsteady transport of dye in a steady flow field is solved to calculate the dye concentration and to produce flow-through curves (FTCs) which are used in evaluating the hydraulic efficiency of settling tanks. The resulting FTC was compared with both measurements and numerical results predicted by various discretization schemes. 1997 by John Wiley & Sons, Ltd.

WAVE ENERGY DISSIPATION IK ROCKFILL

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch F (= gF/u ) as F : 10 ~ 10 . The fetch relations for the growthes of spectral peak frequency u)m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.A solution of finite amplitude long waves on constant sloping beaches is obtained by solving the equations of the shallow water theory of the lowest order. Non-linearity of this theory is taken into account, using the perturbation method. Bessel functions involved in the solution are approximated with trigonometric functions. The applicable range of this theory is determined from the two limit conditions caused by the hydrostatic pressure assumption and the trigonometric function approximation of Bessel functions. The shoaling of this finite amplitude long waves on constant sloping beaches is discussed. Especially, the effects of the beach slope on the wave height change and the asymmetric wave profile near the breaking point are examined, which can not be explained by the concept of constancy of wave energy flux based on the theory of progressive waves in uniform depth. These theoretical results are presented graphically, and compared with curves of wave shoaling based on finite amplitude wave theories. On the other hand, the experiments are conducted with respect to the transformation of waves progressing on beaches of three kinds of slopes ( 1/30, 1/2.0 and 1/10 ) . The experimental results are compared with the theoretical curves to confirm the validity of the theory.Measurements of drift were made in a wind and wave facility at different elevations below the mean water level. The drift profiles were obtained for reference wind speeds, Ur = 3.1, 5.7 and 9.6 m/sec. The measurement technique involved tracing the movement of small paper discs which were soaked in water to become neutrally buoyant at the elevation of release. A logarithmic drift profile is proposed. The water shear velocity, U*w, predicts a surface stress, TS = pw U*S, in agreement with that obtained from the wind shear velocity, s = Pa U*li where pa and pw refer to air and water densities, respectively.The paper describes a procedure for obtaining field data on the mean concentration of sediments in combination of waves and currents outside the breaker zone, as well as some results of such measurements. It is assumed that the current turbulence alone is responsible for the maintenance of the concentration profile above a thin layer close to the bottom, in which pick-up of sediments due to wave agitation takes place. This assumption gives a good agreement between field data and calculated concentration profiles.A section of beach on the south coast of England has been under surveillance for five years, from March 1966 until March 1971. During this period, two permeable groynes of the Makepeace Wood type were constructed. Beach cross sectional areas and rates of accretion were compared before and after groyne construction. The groynes caused a buildup in beach levels updrift.The results of model tests, carried out to evaluate the stability of submarine slopes under wave action are presented. A Bentonite clay was sedimented in a glass walled tank 6 feet long by 0.5 feet wide by 2.5 feet deep. The sedimentation and consolidation processes were studied and sediment densities were measured at various depths in the profile. Vane shear strength profiles were also measured afvarious average degrees of consolidation. Plastic markers were placed in the sediment adjacent to a glass wall so that the soil movements under both gravity and wave induced slides could be documented by photography. Dimensional similitude is discussed and the model test data are presented in a dimensionless form. All instabilities were observed to be of the infinite slope type. Analysis of the data shows that wave action is instrumental in initiating downslope mass movements in gently to steeply sloping off-shore sediments. General lack of agreement between the model test results and published theoretical analyses was found but there was close similarity in the depths and form of failure under wave action and under gravity stresses alone. The loss of stability under wave action is analyzed on the concept that failure is gravity controlled and the soil strength is reduced to a value commensurate with gravity sliding by the cyclic shearing stresses imposed by progressive waves. A method of evaluating the stability of prototype slopes using a model test correlation and field vane strength measurements is proposed. INTRODUCTION Instabilities in submarine slopes have been observed or have been inferred over a wide range of slope angles from less than half a degree up to about 30°. These subaqueous landslides are believed to have caused rupture of submarine cables and to have generated many of the geomorphological features on the ocean bottom. There are numerous records describing these landslides but very few publications discuss the application of the principles of soil mechanics to the analysis of the stability of submarine slopes. Associate Professor of Civil Engineering, Queens University at Kingston, Canada 2 Soils Engineer, Geocon Ltd., Toronto, Canada 3 Associate Professor of Civil Engineering, Cornell University, Ithaca, N.Y.Several mathematical models have been lately presented which describe the tidal wave propagation within an estuary. The existing models derived from the method for damped co-oscillating tides are based on sinusoidal wave profile. Meanwhile a tidal wave which moves upstream, generally exhibits a progressive deformation which tends to unbalance the length of time between flood and ebb tides. The actual profile is therefore no longer sinusoidal. Our investigation uses the potential method, and takes into account the wave amplitude which is usually neglected compared with the water depth. Finally, the velocity potential is obtained explicitely, using a double iterative method. Tidal elevation, particle velocities and trajectories are given by the same computer programmed algorithm. Our study shows that l) the phenomenon can be clearly visualized on the theoretical curves and 2) the magnitude of this deformation is inversely proportional to the water depth, becoming significant when the ratio f|/h reaches the critical value of 1/10. Damping and geometrical effects are also considered and the theory was applied to the St.Lawrence Estuary. A partial positive reflection of the incoming tidal wave is assumed at the narrow section near Quebec, whereas a complete negative reflection is assumed at the entrance to Lake St.Peter. The calculated and observed wave profiles, velocity distributions, and phase shifts are in good agreement.A numerical model is presented to describe the hydromechanics of lagoons connected to the ocean by relatively narrow inlets. Because special attention is given to the flushing, all second order terms in the hydrodynamic equations are retained. The study is restricted to lagoons with a onedimensional flow pattern and water of uniform density. In designing a numerical solution to the equations, the inlet equations are regarded as implicit boundary conditions to the equations describing the flow in the lagoon proper. The advantages of this approach are: (1) the size of the computational grid in the lagoon can be chosen independently of the relatively small dimensions of the inlets and (2) the flow at branching inlets (an inlet connecting a lagoon to the ocean such that branching of the inlet flow can occur) still can be described by a one-dimensional tidal model. The predictive capability of the numerical model is confirmed by favorable comparison between measured and computed particle paths and net transport for a series of laboratory experiments. In the experiments a canal of uniform width and depth is freely connected to a tidal basin at one end and at the other end is connected to the same basin by a submerged weir.

Design of a Hydraulic Control Structure with an in-Spillway Fishpass

The town of Wallaceburg, Ontario, Canada, located on the Sydenham River near its delta at Lake St. Clair, has a long history of serious flooding due primarily to spring runoff and ice jams. In order to alleviate this flooding, the St. Clair Region Conservation Authority has just completed the construction of a flood control dam and floodway. The scheme which is illustrated in Fig. 1 consists of: n n(a) n na nine kilometre floodway with a grass-lined trapezoidal shape, 3H:1V side slopes and a 70 m bottom width; n n n n n(b) n na trapezoidal drop-structure with a trapezoidal stilling basin to regulate velocities in the floodway and control erosion; n n n n n(c) n na 12 m high earthfilled dam; and n n n n n(d) n na concrete control structure with low level sluiceways.